You have chosen wisely. The Ultramarines have some of the fanciest toys in the 31st Milennium.
The first thing to do is remember you're playing 30k, not a reskin of
40k; many assumptions people make about what broad classes of units are good or bad in
40k are utterly groundless. Missile Launchers are relevant (between en-masse deployment, Machine Killers, and 3+-armour
MCs), basic infantry are crucial (and rather than just ObSec you actually can't take objectives without Troops in 30k), Terminators are actually scary (cheaper, better guns, and an endless variety of terrifying Legion-specific versions), and vehicles are much tougher (more hull points, more armour, flare shields, armoured ceramite, fewer D-weapons...).
The Ultramarines are a thoroughly odd Legion, many of the broader advice on how to use the Legiones Astartes list doesn't carry over to them. 30k unit prices tend to include a 'squad tax' to make one maximum squad cheaper than multiple minimum squads (a Tactical squad, for instance, is 125pts for ten models, but only 10pts/model for the next ten, so one twenty-man squad is 225pts rather than 250pts for two ten-man squads), so you'll frequently see 15-20-man blocks in other Legions, but the Ultramarines' Interlocking Tactics rule is set up to reward using more squads over larger squads.
To summarize the Legion's general approach: The Ultramarines' Legion rules and unique Rites of War are designed to give every possible element of your army a small boost rather than pick out a certain playstyle and push it forward. The end result is like playing 4e Space Marines; you can't stand up to any specialist army in the game if you're fighting them where they're strong, so you need to be challenging them where they're weak. Throw curveballs. Salamanders player wants to get up and burn you to death? Stand off and shoot him down at range, or bull-rush Locutarii through the death zone into melee. World Eaters swarm running at you? Stand back and turn on the gunline.
The Ultramarines in 30k end up building all-comers lists out of necessity rather than any objection to skew.
The Ultramarines' selection of unique units tend to do impressive things but come with high price tags and tend to have specialized roles. To summarize:
--Invictarii: Artificer armour, AP2 at initiative, boarding shields, and a leadership bubble. Think of them as a specialized Terminator-killing Terminator unit and you won't be far off.
--Locutarii: Artificer armour, power swords, and jump packs. They're remarkably cheap for a full-power-weapon squad (and remarkably cheap for Legion-specific jump units), but they're quite inflexible and they tend to lose out to more optimal melee loadouts so you'll probably be using them to hunt ranged infantry or thrash troops units.
--Fulmentarii: Artillery Terminators built from the simple desire to copy the Iron Warriors' Tyrant Siege Terminators and make them flashier. They're a bit of a trap; the Ultarmarines' Legion rules are set up to reward a flexible army with a large number of units, so the Terminator unit designed to bait you into spending
700 points on ten Cataphractii with Cyclone launchers sort of undermines the premise. Use them if you're playing a really big game, or if you've got the price discipline to say "No, maybe I'll take, like, six models with autocannons at 400pts instead of going all-in on this one."
And a few final words on building armies on a budget:
Ebay is your friend.
GW wants to sell you the Calth/Prospero component boxes at 1.5-2x what the sprues parted out of the full boxes go for on Ebay. You may or may not wish to indulge them in that.
The degree to which Forge World models are necessary is heavily dependent on how snobbish your playgroup is. Some people object to normal
40k plastics showing up in a Heresy game, some don't. If you're playing with the latter sort you almost don't have any issues; just bring along ordinary Mk.VII assault marines (and Vanguard Veterans to use as Locutarii). Most of the 30k motor pool overlaps with the
40k motor pool, all your Rhinos, Predators, and some Land Raiders can just hop straight over.
If you do run into people who grumble about the lore-friendliness of your army you may be able to shortcut Forge World prices somewhat by modifying existing models with greenstuff;
http://www.bolterandchainsword.com/topic/262448-horus-heresy-tutorials-thousand-sons-magistus-amon-160217/ is a tutorial for making various Heresy armour out of normal
40k plastics that should lend itself to modifying units that don't come in Calth/Prospero.
The only things you really can't (or shouldn't, given how awesome they are) dodge
FW prices for are era-specific vehicles and the Character Series (Guilliman is the only Ultramarine character there so far). Most people working on a budget tend to end up with a couple of era-specific vehicles as centerpieces (the cliche
FW purchase is a Spartan to put your Primarch-deathstar in and a Sicaran or two because they're good general-purpose tanks).
(Before you ask me whether you can just use the plastic Triumvirate Guilliman I suggest you look at the two models and ask yourself the question again. To my mind there's an obvious answer. You may disagree, and if you do good for you, you're in Australia so I don't have to worry about ever having to look at the Triumvirate Guilliman.)